Question

For the equation y = 3x² - 4x + 11, choose the correct application of the quadratic formula.

a) 3 + √(3² - 4(11))
b) -4² - 4(3/11)
c) -3 ± √((3)² - 4(-4)(11)) / 2(3)
d) 4/3 - 4(3 × 11)

Answer 1

The correct application of the quadratic formula for the equation y = 3x² - 4x + 11 is 4/3 - 4(3 × 11).

Step-by-step explanation:

The quadratic equation y = 3x² - 4x + 11 can be solved using the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / (2a)

For this equation, a = 3, b = -4, and c = 11. Substituting these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)² - 4(3)(11))) / (2(3))

x = (4 ± √(16 - 132)) / 6

x = (4 ± √(-116)) / 6

The expression inside the square root (√(-116)) is negative, which means that the equation has no real solutions. Therefore, the correct application of the quadratic formula for this equation is option d) 4/3 - 4(3 × 11).